This work is a numerical investigation on the influence of viscoelastic effects on the aerodynamics of integrally actuated membrane wings. For that purpose, a high-fidelity electro-aeromechanical computational model of wings made of dielectric elastomers has been developed. The structural model is based on a geometrically non-linear description and a non-linear electro-viscoelastic constitutive material law. It is implicitly coupled with a fluid solver based on a finite-volume discretisation of the unsteady Navier–Stokes equations. The resulting framework is used for the evaluation of the dynamics of passive and integrally actuated membrane wings at low Reynolds numbers under hyperelastic and viscoelastic assumptions on the constitutive model. Numerical simulations show that the damping introduced by viscoelastic stresses can significantly reduce the amplitude of membrane oscillations and modify key features in the coupled system dynamics. The estimated wing performance metrics are in good agreement with previous experimental observations and demonstrate the need of including rate-dependent effects to correctly capture the coupled system dynamics, in particular, for highly compliant membranes.